All Questions
Tagged with newtonian-gravity classical-mechanics
112
questions
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How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
- 117
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1
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Is quadrupole contribution to gravitational potential the sum of the contribution of all $m$ values?
Many of the sources I find on multipole expansions seem to be about electric potential and involve matrices. However, in my classical mechanics class we have not used matrices for multipole expansions ...
- 414
-4
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2
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117
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Is Newton's gravitational acceleration centripetal instead of attractive?
In 1845 W. R. Hamilton demonstrated [1] by the use of the hodograph representation that the velocity of any Keplerian orbiter is the simple addition of two uniform velocities, one of rotation plus ...
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2
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40
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Is there a way to express the collisionless boltzmann equation in terms of positions, velocities, times, without the distribution function?
Suppose I have data that represents a field of positions and velocities. If the distribution function (DF) for the data is $f(x,v,t)$, I know that the DF must obey
$$\frac{\partial f}{\partial t} + \...
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1
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In one formula of orbital velocity for circular orbit it has inverse relation with radius while in critical velocity relation it has direct. Why?
In one formula of orbital velocity for circular orbit it has inverse relation with radius
$$v=\sqrt{\frac{GM}{r}}$$
while in critical velocity relation it has direct
$$v=\sqrt{gr}$$
Why?
2
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1
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267
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How to calculate the period of non-circular orbits?
How to calculate the period of non-circular orbits?
By conservation of mechanical energy:
$$
E = -\frac{GMm}{r} + \frac{1}{2}\mu \left ( \dot{r}^2 + r^2 \dot{\theta}^2 \right )
$$
By the conservation ...
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1
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41
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Potential energy change is not negative? [closed]
$\Delta U = -(W_{earth} + W_{ball})$
$W_{ball}$ is almost 0, as earth's displacement by the falling ball is super small, so $\Delta y$ of the earth could be negligible and $W_{ball} = 0$. so:
$\Delta ...
- 137
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2
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224
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Laplace's equation doesnt reproduce Newtonian gravitational potential
Newton's law of gravitation describes the gravitational potential produced by a mass $m$ as : $G(r)=-k\frac{m}{r}$.However if you solve Laplace's equation for the gravitational potential in polar ...
user369585
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111
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Measuring the effect of spin of a tennis ball on its trajectory
Upward spin (lift) applied to a tennis ball will shorten its trajectory.
Are mathematical calculations and actual experimental results on this available somewhere?
If not, does anyone know how to ...
- 17
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3
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182
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How to prove that a drop of water in the weightlessness of space is round in shape?
How to prove that a drop of water in the weightlessness of space is round in shape theoretically? More specifically, how to prove that a drop of water in the weightlessness of space is round in ...
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How to obtain the equations of motion and trajectory of a particle from the effective potential?
In a certain problem regarding motion of a particle in a gravitational field with axial symmetry, I have an expression of an effective potential $\Phi_{eff}(r,\theta)$. Now, I am interested to study ...
- 2,015
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2
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158
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Why does the Lagrangian not show particle-interaction? Why are normal/tension forces not considered?
(1) For formulating a lagrangian for a system of particles compared to one free particle, we start with the kinetic energy and formulate a potential energy term that is in terms of each of the radius ...
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43
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Why is it important to release energy as quickly as possible to perform a vertical jump?
Let's assume that we create this mechanism, where we must decide if the actuating cylinders are double-acting hydraulic or pneumatic with a spring inside.
the goal is for the mechanism to suddenly ...
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1
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82
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Conic Section in Newton's Cannonball Problem
From the Classical Mechanics Lecture Notes by Helmut Haberzettl, we know that in Newtonian Mechanics, the solution to Kepler's problem can be parametrized as a conic section equation
$$r(\varphi)=\...
- 381
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6
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95
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Free falling bodies in the absence of external forces
We know that if two balls $B_{1}$ and $B_{2}$ having masses $m_{1}$ and $m_{2}$ respectively and suppose $m_{1}$ is sufficient greater than $m_{2}$. In daily life observation, we see that both the ...
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How much time after will two oppositely charged particles collide for both gravitational force and electrostatic force?
Suppose two point objects charged with opposite charges $q_1$ and $q_2$ at a distance $r$ in a vaccum.
So, the net electrostatic force on both objects $= F_c = \frac {q_1q_2}{4π\epsilon_0r²}$ [$\...
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3
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178
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Why gravitational potential away from a planet increases?
textbooks----
"potential increases towards infinity and is maximum at infinity"
But that is true only when we are seeing potential w.r.t Earth
EXPLANATION---------
So , as we know that ...
- 444
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57
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If the change in potential enegry is equal to the negative of the work done, then this principle isn't consistent here in the case freely falling body
Let us assume that a body of mass $m$ falls from height $h_1$ to $h_2$ :
Here the Work done by gravitational force (Conservative force) is :
$$\mathrm{Force \ ×\ Displacement} = mg \ (h_2-h_1) \tag1$$
...
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114
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What is the effective potential for photons in Newtonian gravity?
I am confused about the movement of photons and their trajectory, I hope you can help me:
What kind of path does light follow in Newtonian gravity?
What is the effective potential for photons in ...
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224
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Equation of motion of a classic inverted pendulum in free fall
I was thinking in this interesting problem:
Suppose we have this inverted pendulum:
But without this control force $F$ and the system would by loose from a height $h_0$, with initial velocity $0$ ...
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2
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3k
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What happens when the PE equals to zero in the potential energy vs intermolecular distance graph? [closed]
In the potential energy versus inter molecular distance graph, we know that atoms/molecules/particles want to be at optimum distance from each other ie $r_0$ and to the left of this position in the ...
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699
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Why in binary star system the 2 bodies revolve around their center of mass?
Can you prove it mathematically?
Is it just an observation?
I know the force between them is $\frac{Gm_1m_2}{r^2}$.
Centripetal force on any one of them is $\frac{mv^2}{r_1}$, where $r_1$ is radius of ...
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120
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How do you find the position at which three particles obey $m_1 a_1 = m_2 a_2$ if two of the particles form a composite body?
From Classical Mechanics by Kibble:
Consider a system of three particles, each of mass m, whose motion is
described by (1.9). If particles 2 and 3, even though not rigidly bound
together, are ...
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1
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648
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Newton's first law - elevator lift upward and downward force [duplicate]
Why does $F_c$ is equal to $F_g$ and why $F_c$ isn't greater than $F_g$? $F_c$ is moving it upward right, so the force must be greater than gravity to pull it upwards I think.
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188
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Physical interpretation of the symmetry for the Runge-Lenz vector
In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...
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1k
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When is the effective potential equal to the total energy?
I have a question about the energy of a particle in orbit due to a gravitational attraction. The effective potential given by the gravitational force is defined to be
$$
U_{\text{eff}} = \frac{L^2}{...
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82
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Exact distance travelled by an object due to gravity only
I am aware of the fact that for two point masses in space, the time that it will take for them to collide is, T=$\pi \sqrt{\frac{r_i^3}{8GM}}$, where M is the sum of the 2 bodies' masses, $r_i$ is the ...
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Justification for the nature of planet's orbit in gravitational field!
In kleppner Mechanics in the chapter central force he derived the polar form of orbit for gravitational force as illustrated below: (first two equations are derived from fundamentals of central force)
...
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43
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Variable mass of orbiting body
Considering an object orbiting earth at radius $R$ and speed $v$, at one moment in time the mass of the object starts to decrease, what will happen to the object in terms of speed and orbit?
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A thought experiment to prove that Newtonian gravity is incomplete [duplicate]
A particle is at rest in one frame having mass $m$. It'll attract another mass proportional to its mass ( newtons law) .
We jump into another frame moving close to speed of light. In this frame it's ...
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